# Bounds on Options

Discussion in 'CM2' started by N_Exam, Jan 26, 2020.

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1. ### N_ExamVery Active Member

Hi,

Question mainly for a tutor but would be good if others gave their answers :
Bounds on Options, CT8 exam, April 2012, Q4. (Also revision book 5, Q23)

Qa)
Question on theory in (4i): Why would the call holder receive a dividend payment? Surely the stock holder receives and keeps the dividend and just gives the stock to the call holder if exercised?

Qb) Question on (4i): I understand that stock holder, portfolio B, has at maturity S_T + De^(rT1). I do not understand why at time 0 the stock holder only has S_T. Why do they not have 1 dividend paying share and a discounted dividend, S_T + De^(-rT1).

Qc) Question on (4ii), similarly to the above question, at time 0 why does the holder of the put not have a discounted dividend, De^(-r(T-T1)), but has this dividend at maturity?
Also, why cant we use the call put parity in this question?

Thank you for answering.

2. ### mugonoTon up Member

Caveat: I haven’t read / seen the quoted IFOA exam paper / revision question. Nevertheless, some responses below.

A. Call holders do not receive the dividend; you’d have to own the underlying in order to receive a physical dividend. The dividend is however priced into the value of the call.

B. The price of a share at time 0 is s(0). You may need to be careful with your use of notation. The price of a share at time t (where t=0,1,2,...,T) is s(t).

A share price includes its dividend until the ex dividend date. The time 0 price therefore contains all future cash flows. Adding explicit cash flows in the manner you suggest in part B would result in a double count.

Investors who purchase the stock after the ex dividend date are not entitled to the dividend; and the share price reduces by the amount of the dividend as a result.

By time T, the dividend has been paid. The total value of the portfolio of an investor who held the stock on the ex dividend date would need to add the explicit dividend to determine its total return. The dividend payment compensates for the reduction caused when the share priced fell to exclude the dividend.

To summarise; think of S(0) as a gross of dividend price and S(T) as a net of dividend price.

C. As explained in A, holders of puts / calls to not accrue a physical dividend. The dividend will however be reflected in the put / call price.

Put / call parity described an exact relationship between a European style put and call of the same expiration, strike and underlying. The relationship holds under the assumption that there is no arbitrage.

The question is a discussion on the bounds that an option must satisfy more generally.

Last edited: Feb 3, 2020
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